Have now had a good listen to this and it's definitely not the PRE settings causing the problem.
I turned both master sends off, and the click was still there. Then retried with all the PREs set to OFF and individual levels off just to be sure, and no difference. The assigns all seemed ok.
The click sounds like an electronic one, as opposed to stray pickup from the mic, and it appears at the point where all the vocal tracks stop.
The interesting thing is if I rewind a few seconds and play just the end of the song, the click is not there, but if I rewind to the beginning, the click appears.
Both tracks 1 and 2 played in isolation produce the click. I didn't try any others as it means playing the track through from start to finish each time!
My hunch is this is being caused by corrupted file(s) on the card.
I tried a 'delete unused' on the song, which reduced the song size slightly, and it then got in a complete knot playing back, with file errors and read timeout messages. Had to power off to get back control.
Note that my machine isn't quite the same as yours - I misread your avatar gear details and thought you had a 32sd, but it's a 24sd, so I think you should get a second opinion with another 24sd owner.
Just as an aside, one thing I never noticed before on these machines was tiny blobs at various points on the coloured track lines in the timeline view (they're very subtle - same colour but brighter). I wonder if this indicates edit/punch-in points?
Finally, the harmonies on this song are superb!